I need help please with the following question.

(a) Use the Intermediate Value Theorem to show that the equation x + sinx = 1, has at

least one solution in the interval [0,1].

(b) Find an approximation of the solution with an error of at most 0.05.

I have attempted the question as follows:

Part (a)

f(x) = x + sinx -1

f(0) = 0 + sin(0) -1

= 0 + 0 -1 = -1

f(1) = 1 + sin(1) - 1

= 1 + 0.017 -1 = + 0.017

Since 0 occurs between -1 and +0.017 the IVT tells us thatthere must be a number c in [0, 1] and that f(c) = 0

Therefore there exists (at least) one solution.

Part (b):

f(0) =-1, f(0.1) = -0.9, f(0.2) = -0.8, f(0.3) = -0.7,f(0.4) = -6, f(0.5) = -0.5, f(0.6) = -0.4, f(0.7) = -0.3, f(0.8) = -0.2, f(0.9)=-0.08, f(1) = +0.02

Therefore the root lies in the interval [0.9, 1]

Therefore the midpoint(0.95)approximates therootwith anerror of at most 0.05

Your comments would be welcomed.